Evolution
Not to be confused with "Evilution".
Basic Description
While the term is used in various ways, in this context "evolution" refers to change of inherited traits among reproductive populations over generations, which is summarily defined as "descent with [inherent genetic] modification" as coined by Charles Darwin. It is a natural phenomenon that encompasses the diversity of all life. One of the driving mechanisms behind this process is "natural selection".
The theory of evolution (ToE) is the scientific model that explains how and why biological evolution occurs, as well as explaining the unity and diversity of life (not its origins) by concluding that every known species extant or extinct, is the result of evolution through common descent (and a few other processes such as "horizontal gene transfer" and "endosymbiosis"). As a result of the overwhelming evidence in favor of the theory, it represents the consensus of the scientists in the field of biology and science in general, thereby making it one of the strongest and well-supported theories in science. The theory of evolution is the very backbone of modern biology and understanding evolution has become a fundamental aspect in that particular field of science.
Understanding evolution (especially how it works) isn't easy. In order to adequately understand evolution, you need to have a basic understanding of many different things, including cellular biology, genetics, anatomy, geology, palaeontology, taxonomy, and more. It is a very complex subject and passing biology classes in college requires following many lessons on evolution, depending on what schools you are talking about. Many notable scientists throughout history have devoted their entire careers to this very subject, and many still do. Despite this, there are quite a few people who dismiss the entire scientific paradigm by asserting that evolution is "just a theory, not a fact" (among other asinine statements), as if they know better than every expert anywhere ever. The bulk of this category consists mainly of scientifically illiterate morons.
Etymology and Semantics
The word "evolution" (from the Latin root word "evolutio", meaning "to unroll" or the act of opening a book) traces its origins back to the 17th century when it was used to mean various things, including the description of physical movement, such as a tactical wheeling maneuver to realign the troops or ships. In early science, it was used as a synonym of "growth" and "development".[1] Eventually the term came to be used in a more general way to describe progressive change. Ironically, Charles Darwin didn't prefer this word to describe the process of population level changes across generations. He used the phrases "transmutation by means of natural selection" and "descent with modification". Darwin used the word "evolution" only once in his book "On the origins of species".
"There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved."
Contemporary scientists, such as Julian Huxley (aka Darwin's Bulldog), adopted the term "Evolution" and is still in use by scientists today as the accepted technical term, although scientists do use the word in different ways. Cosmologists often refer to the process of how stars are "born", change and "die" as "Stellar Evolution". Under this general and rather nebulous usage, "evolution" simply means "change over time".
Creationists often exploit this semantical aspect of the term to misrepresent evolutionary theory. One infamous example is the "6 types of evolution" by Kent Hovind, wherein big bang cosmology, nucleosynthesis, stellar/planetary accretion, abiogenesis, and biological evolution are all erroneously lumped together under one banner called "evilution(ism)" as if they were all part of the same theory wherein "everything came from nothing without God". The creationists do this to create the illusion that their denial of science is limited to just one thing, not to multiple aspects of many different scientific theories spanning many independent fields of science. They also do this to make it seem like a person cannot accept biological evolutionary theory without also accepting all the other theories that they have equated with ToE, meaning that they must also accept that the Genesis isn't literal and that God doesn't exist, so a person cannot be a "true" christian and also accept evolutionary theory. Of corse, this is also erroneous and is the 1st Foundational Falsehood of Creationism as stated by AronRa.
Creationist attempts to straw-man evolution is an easy excuse to explain why most people have such a fucked-up view of what evolution is, but it isn't always their fault. Even popular media that seem to promote evolution as a positive, progressive thing such as "Pokemon", "The X-men" and various movies that use evolution as a trope, only spread misconceptions more often than correct them.
Unless the context is specified to be something else, under the modern biological context "evolution" refers to an aspect of population genetics - in which case, it is summarily defined as "Descent with Inherent [genetic] modification". Paraphrased for clarity, it is a process of changing allele frequencies among reproductive populations over generations, which leads to changes in the morphology and/or physiology of descendant subsets. When compiled over many generations, these changes can expand biodiversity when increasing variation between genetically-isolated groups eventually lead to one or more descendant branches that are increasingly distinct from their ancestors and/or cousins. - Or if you prefer, the process by which life forms diversify via "descent with modification".
A broader definition can also be made that includes other processes that parallel the evolution of life forms, but don't involve life. Viruses are not considered to be alive, but they do reproduce imperfectly and inherit genetic material, so they also can evolve. Self-replicating molecules have the potential to evolve as well, and is posited to be one factor that explains the origin of life. While evolution may be a part of abiogenesis by this broader definition, this isn't true the other way around (abiogenesis is part of evolution) since abiogenesis involves chemical processes that don't count as evolution. Other examples are computer programs such as genetic/evolutionary algorithms and how human language has changed. The evolution of language parallels the evolution of life almost perfectly such that it can be used as a very good analogy to explain to laymen what evolution is and how it works.
Explaining Evolution
Quick Historical Overview
The idea that animals could descent from different animals (including humans) wasn't made-up by Charles Darwin. Earlier concepts of it existed, most of them were dead wrong and laughable compared to our current understanding, which is just the case with the earliest concepts of other scienctific paradigms.
From Antiquity to Medieval Times
Greek philosophers proposed their own evolutionary ideas. One of them was the pre-Socratic Greek philosopher Anaximander of Miletus, who proposed that the first animals must have lived in water and that the first land-dwelling ancestors of humans would've been amphibious, spending most of their time in the water to give birth and partially to forage onto land. That was quite accurate, surprisingly so, especially considering that this man lived over 2500 years ago. However, later and more influential philosophers proposed that all things, not just living ones, were immutable by divine design according to Plato's essentialism, and Aristotle proposed that everything was part of a hierarchy called "scala naturae" (Great Chain of Being), sometimes erroneously called "the evolutionary ladder". This hierarchy was constructed according to the degree of "perfection", with "higher forms (of life)" at the top. Obviously, humans were put as the highest form among living things, just below divine beings. The Islamic world preserved these ideas and reintroduced them to medieval Europe, where these ideas were accepted by Christian thinkers, such as Thomas Aquinas, and later adapted to fit their theology by putting God on top of the scale and Hell at the bottom. Life forms were organized as species, each species occupied its own place. As it was believed that every species was created by God to be unchanging, species moving (or evolving) from its position to a higher or lower one wasn't considered as a possibility.
References
Extras
MrIntelligentDesign's comments have been mirrored to his own page, due to its lack of scientific accuracy and coherency. (After MrID wrote the same thing for the second time after removal) Because this page is not intended to be a debate forum, his comments are removed again, but they are still on his own page, where people can still see it (so it isn't censorship). Sorry Edgar, do this on your own page or somewhere else. It doesn't belong here. (After MrID wrote the same thing again for the third time after removal) Dear Edgar, People can clearly see here above that you wrote something on this page. They can click on the link and see what you wrote, so you don't have to put your shit back on this page again and again. If you do place it here again, I will (unfortunately) private the page so that you will not be able to do it again until you accept that this page is not a place for you to pontificate. That's why you have your own page. Please don't force my hand.